Basic-Questions about Quantum terms

[Anglea]

I realize my questions are very basic, that is because my background is a bit different, and I have to understand these terms to be able to do my work I guess all people here are famiilar with these basic things, please help me, I would appreciate your time ...
what we mean if we say need to take wave functions as a Gaussian processes?what is Ensemble average?Stochastic prosses? due to the dispersion relation in quantum mechanics the eigenvalues are degenerate, how this is related to each other??what we mean by clean system, and dirty state??

 

[IPart]

Wow. The answer may take a course!

Wave functions may be represented by "Gaussian wave packets": NOT gaussian processes. In fact they may be represented in the basis of any set of complete functions.

Consider a very large (tending to infinity) number of identically prepared systems with given system parameters (say T,V, and P). Then the theoretical idea of taking an average over all these systems of some other physical observable, is called "ensemble averaging". Of course, there is a quantum mechanical analogue but that may be too much information for now.

 

[Anglea]

Wave functions may be represented by "Gaussian wave packets": NOT gaussian processes. In fact they may be represented in the basis of any set of complete functions.

appreciate your time, as I am new comer to this field I have read many articles, but with nothing! so I guess it is better if anyone could give me idea of the meaning to be able to go on myself for more details.

what is the advantage of taking the wave function as a "Gaussian wave packets", is this somehow related to the normalization .

Consider a very large (tending to infinity) number of identically prepared systems with given system parameters (say T,V, and P). Then the theoretical idea of taking an average over all these systems of some other physical observable, is called "ensemble averaging". Of course, there is a quantum mechanical analogue but that may be too much information for now.

if we have a billiard how we can construct such ensemble.
can anyone tell me what this sentence mean

due to the dispersion relation in quantum mechanics the eigenvalues are degenerate

.
What is the difference between clean and dirty states??

 

[Anglea]

what is the difference between the scars and the nodal lines ?

 

[Naty1]

Your questions are NOT at all basic...what are you studying that brings so many advanced concepts to the forefront?? Without a strong, graduate level math background, you'll be hard pressed to understand the answers to much of what you ask...if you are just looking for intuitive, layman's explanantions, you'll do a lot better here.

For an idea of renormalization, try wikipedia:
http://en.wikipedia.org/wiki/Renormalization

It's a mathematical device for eliminating certain divergences, that is, what would other wise be infinities...for example sometimes a pair of infinities can be canceled by substraction...Feynman called it "hocus pocus"...somebody else a "subterfuge" (I suspect proper mathematicians find it totally abhorrant) ...an example the result of field interactions of point particle approximations becoming infinitly strong at sub atomic distances...I think perturbation theory also runs up against some of these infinities even when they are used to avoid such problems and unsolvable (lengthy/complex) complete mathematical formulations.

(an approximate solution might be expanding a complete (and complicated) formulation to a Taylor series (to simplify) and then approximating by using only the first (most significant) term or two...

 

[Fredrik]

What is the difference between clean and dirty states??

I'm not familiar with those terms. Do you mean "pure" and "mixed" states? See e.g. this Wikipedia article.

Naty1, I think (s)he meant "normalization" (i.e. making sure the norm of the wave function is 1), not renormalization.

 

[Anglea]

I'm not familiar with those terms. Do you mean "pure" and "mixed" states? See e.g. this Wikipedia article.

I came across these terms when I read a about regular system and ergodic geodisc? Is the clean system just the regular system, or they are different? what is the ergodic??

Naty1, I think (s)he meant "normalization" (i.e. making sure the norm of the wave function is 1), not renormalization.[/QUOTE]yes I mean the Normalization.

p.s.It would be highely grateful if you could not refer me to Wiki.

 

[Anglea]

Your questions are NOT at all basic...what are you studying that brings so many advanced concepts to the forefront?? Without a strong, graduate level math background, you'll be hard pressed to understand the answers to much of what you ask...if you are just looking for intuitive, layman's explanantions, you'll do a lot better here.

For an idea of renormalization, try wikipedia:
http://en.wikipedia.org/wiki/Renormalization

It's a mathematical device for eliminating certain divergences, that is, what would other wise be infinities...for example sometimes a pair of infinities can be canceled by substraction...Feynman called it "hocus pocus"...somebody else a "subterfuge" (I suspect proper mathematicians find it totally abhorrant) ...an example the result of field interactions of point particle approximations becoming infinitly strong at sub atomic distances...I think perturbation theory also runs up against some of these infinities even when they are used to avoid such problems and unsolvable (lengthy/complex) complete mathematical formulations.

(an approximate solution might be expanding a complete (and complicated) formulation to a Taylor series (to simplify) and then approximating by using only the first (most significant) term or two...

appreciate you time, JUST GET CONFUSED WHICH Q you have answered, I mean normalization?

 

[Anglea]

can anyone please show me the difference between the A causal Green's function causal Green's function ??

 

[Anglea]

can anyone explain to me what they mean by a separable system in co-ordinate space? and what the meaning of (classical integrability does not require the quantum separability)